Neither CX nor AA will issue a ticket with only 50 minutes domestic to int'l travel time at LAX, as the legal transit I think is 90 minutes. Fifty minutes is really pushing it anyway. Even if the AA flight arrives on time, it takes 10 minutes to speed from the gate to TBIT. The lines to get through security at TBIT, even the priority lines, can easily take 20-30 minutes. The slightest snag and you are sunk.

Anyway, upon arrival at TBIT, you should still check in with CX and make them aware of your baggage tags (they will enter them in the computer and make sure that they have arrived and are loaded). When you board, you can always ask the agents at the gate to confirm your bags are on board. Many times they've offered this info to me w/o me even asking.

If you split the tickets and you miss the CX flight, neither airline would be required to protect you.

As for interlining baggage from Delta, if it makes you feel better to claim your luggage and lug it to TBIT, after which you need to put it through the X-ray machine and then take it to the ticket counter, then do it. However, I think Delta is a competent airline and they deal with interlining bags countless times a day. Again, give CX your baggage tags when you re-check in and they'll call downstairs to keep an eye out for your bags and put the priority tags on them. I personally wouldn't give a second thought to interlining my bags, especially on a 3.5-hour layover, but of course everyone's different.